1. Field of the Invention
The present invention relates to the field of digital signal filtering, and more particularly, to a first order recursive digital filter.
2. Description of Related Art
Digital filters are used for converting a sequence of numbers representing an input signal into another sequence of numbers representing an output signal. During this conversion process, the character of the input signal changes in some prescribed manner. Digital filters are generally linear and time-invariant, and can usually be fabricated from conventional digital hardware such as adders, multipliers and shift registers. Digital filtering can also involve a process in which a computer is used to generate a filtered output signal from a sampled input signal.
Digital filters are generally designed by selecting a desired transfer function and then implementing the transfer function using a variety of realization procedures. Depending on the realization procedure used, digital filters are often categorized as being either "recursive" or "non-recursive". The term "recursive" is used to describe filters which are generally realized by a circuit or a process in which the output of the filter is a function of a linear combination of the input signal as well as a prior input and a prior output signal. A filter is "non-recursive" when the filter is realized by a circuit or process in which the output signal is a linear function of only the past and present input signals. While filters realized in non-recursive form have good phase characteristics, such realizations often require a large number of components when compared to recursive implementations.
First order recursive digital filters are often realized by using canonical form representation. According to this realization, the output of the filter is delivered to a multiplier after passing through a delay element. The output of the multiplier is then delivered to an adder which sums the subsequent filter input signal with the multiplier output. Because multipliers are relatively slow, however, hardware or software implementation of these filters are often relatively inefficient in terms of speed. Further, the performance of such filters often decreases as the number of shifting operations increases. Multipliers are also often more expensive than other components such as adders, which tends to increase the relative cost of filters in which multipliers are used. Finally, there are some technologies, such as ECL and GaAs, in which effective multipliers do not currently exist. Although some non-recursive filters such as the one disclosed in U.S. Pat. No. 3,979,701 attempted to avoid using multipliers, they were not generally capable of direct implementation as recursive filters.